Gamma Interactions and Gamma Spectroscopy with Scintillation Detectors
1. Gamma Interactions
and Gamma
Spectroscopy with
Scintillation Detectors
By
Dan Maierhafer
EES611
March 14, 2001
2. Table of Contents
I. ABSTRACT.....................................................................................................................4
II. INTRODUCTION..........................................................................................................4
III. THEORY......................................................................................................................5
A. GAMMA RAY INTERACTIONS IN MATTER...............................................................................5
1. Photoelectric Absorption...........................................................................................5
2. Compton Scattering...................................................................................................5
3. Pair Production........................................................................................................7
B. ENERGY SPECTRA.............................................................................................................7
1. Photoelectric Absorption...........................................................................................7
2. Compton Scattering...................................................................................................8
a) Compton Edge......................................................................................................9
b) Backscatter............................................................................................................9
3. Pair Production........................................................................................................9
C. RESPONSE FUNCTIONS.......................................................................................................10
1. Small Detectors.......................................................................................................10
2. Very Large Detectors..............................................................................................10
3. Intermediate Size Detectors.....................................................................................10
D. ENERGY RESOLUTION......................................................................................................12
IV. EXPERIMENTAL DESIGN AND PROCEDURE...................................................13
A. 2” X 2” NAI:TL SCINTILLATOR SETUP AND PROCEDURE...........................................................13
B. 5” X 5” NAI:TL SCINTILLATOR SETUP AND PROCEDURE...........................................................14
C. EQUIPMENT USED...........................................................................................................15
V. RESULTS AND DISCUSSION...................................................................................16
A. SINGLE CHANNEL ANALYZER............................................................................................16
1. Identify Peaks in Cs-137 Pulse Height Spectrum taken by SCA................................16
2. Determine Detector Resolution................................................................................16
3. Compare SCA Spectra with MCA Spectra................................................................17
B. MULTI-CHANNEL ANALYZER............................................................................................17
1. Detector Resolution using Cs-137............................................................................17
2. Detector Resolution using Na-22.............................................................................17
3. Unknown Identification...........................................................................................19
4. Determine the Activity of the Cs-137........................................................................19
VI. CONCLUSIONS.........................................................................................................19
A. 2” X 2” SCINTILLATOR COMPARED TO 5” X 5” SCINTILLATOR...................................................19
B. METHOD OF DETERMINING UNKNOWN.................................................................................20
2
4. I.Abstract
This paper investigates the response of an NaI:Tl scintillator and
photomultiplier tube combination Gamma Ray Detector. Two sizes of
crystal were used in this experiment. The first size was a 5”x5”, and the
second size was a 2”x2”. The solid crystalline detector was coupled with a
photomultiplier tube and other conventional radiation detection electronics
to measure pulse height, count rate, energy resolution, dead time, and
background count rate using nominal radioactivity standard sources. Plots
of Count Rate versus Channel Number were made for Cs-137, Co-60,
and Na-22 known sources. The Full Energy Peak was calibrated on these
graphs using data from the RADECA program. The Energy Location of
important features of these nuclides were located and listed in a table in
this report. A curvefit plot was made of Source Gamma Ray Energy vs.
Channel Number in order to find the Full Energy Peak of two unknowns.
This Full Energy Photon Peak was then used to identify the two
unknowns.
II.Introduction
The subject of this report is the Spectroscopy of Gamma Rays using the
NaI:Tl scintillator and photomultiplier tube detector combination. These
devices became popular in the early 1950’s, because they were able to
make high resolution, high efficiency measurements in a portable detector.
Even after the discovery of a multitude of other scintillating materials,
NaI:Tl still remains popular because of its efficient energy conversion from
photons to electricity.
In this laboratory exercise, we used a NaI:Tl scintillator-photomultiplier
device to detect and differentiate between the gamma ray energies of
various sources. We also differentiated between the features and the
measurement anomalies of the gamma ray spectra and found the Full
Energy Peaks described later. Next we used the curvefit of the Full
Energy Peak vs. Channel Number from the known sources to identify two
unknown source Full Energy Peaks of using Channel Number as the
independent variable.
4
5. III.Theory
A.Gamma Ray Interactions in Matter
Gamma Rays are a type of ionizing radiation emitted from the nucleus
of an atom with energies in excess of 10 KeV (Fjeld). Gamma rays
can interact with matter in three main ways depending on how much
Incident Energy the Photon contains. The three main ways are:
Photoelectric Absorption, Compton Scattering, and Pair Production.
1.Photoelectric Absorption
Photoelectric Absorption is prevalent when photon energies are below
100’s of KeV (Knoll, pp.308). The mechanism is an inelastic collision
in which the gamma ray collides with a bound electron and causes it to
ionize. The electrons usually affected are in the K-shell. Because the
collision is inelastic, the kinetic energy imparted to the ionized electron
is equal to the incident energy of the gamma ray minus the binding
energy of the electron. Equation 1 shows how to find the Kinetic
Energy of the ionized electron.
Equation 1: KE e − = Eγ − E binding
The electron that escapes from the atom called a photoelectron. The
vacancy created by the escapee electron is filled from one of the upper
shell electrons. When this occurs, the difference in electron binding
energy from the upper to the lower level is emitted as either an X-ray
or an Auger electron. If an X-Ray carries away the binding energy, it
typically travels about a millimeter before being reabsorbed through
photoelectric interactions. If an Auger electron escapes carrying the
energy, it will also have limited range because the energy is typically
very low (in the eV range) (Auger).
2.Compton Scattering
Compton Scattering is the main interaction when gamma ray energy is
from the 100’s of KeV to about 5 MeV. This interaction occurs with an
outer shell electron of very low binding energy. The mechanism is like
that of an elastic collision between two particles. If the incident gamma
ray strikes the electron at an angle, the electron scatters the incident
5
6. gamma ray at another angle, Θ. At the same time, this electron is
deflected by an equal angle in the other direction.
Eγ’
Θ
Eγ
Figure 1. Diagram of Compton Scattering Event
The angle Θ depends on the grazing angle between the electron and
the incoming gamma ray. The energy of the scattered gamma ray
photon is found by using Equation 2. The energy of the scattered
recoil electron is found by using Equation 3.
Eγ
Eγ ' =
1 + Eγ
Equation 2:
511 KeV ∗ (1 − cos Θ )
Eγ
511 KeV * (1 − cos Θ )
Equation 3: E e − = Eγ *
1 + Eγ
∗ (1 − cos Θ )
511 KeV
There are two extreme cases in this type of gamma interaction. The
first case happens when Θ = 0 degrees, or the gamma ray just barely
grazes the electron. From Equation 2 and 3, it is known that the recoil
electron has almost zero energy, while the scattered gamma ray has
almost the same energy after and before the interaction.
The second interaction of interest occurs when Θ = 180 degrees. This
is a head on collision, where the incident gamma ray is scattered
6
7. backwards where it came, and the electron recoils along the path of
the incident gamma ray.
3.Pair Production
Pair Production occurs with high-energy gamma rays between 5 and
10 MeV. It is a type of energy to matter conversion that occurs near
the high electric field located in the vicinity of the protons of the
absorbing material. In this interaction, the gamma ray is transformed
into an electron-positron pair. Einstein’s equation describing energy to
mass conversion is employed as shown in Equation 4 to determine the
minimum energy required for this type of interaction.
Equation 4: E = m * c 2
Since the mass of an electron and a positron are both equal to m0,
then the minimum energy required to create the particles will be 2*E,
which corresponds to 2*m0*c2. If the incident gamma ray has any
additional energy, it will be imparted to the two particles as kinetic
energy. This is shown symbolically in Equation 5.
Equation 5: E e − + E e + = Eγ − 2 * m0 * c
2
After the electron-positron pair is created, the electron escapes and
interacts with matter via an ionization, excitation, disassociation, or free
radical formation. The positron is an antimatter particle, and once it
slows down to the thermal energy of a normal electron in the absorber,
it combines with an electron and creates two annihilation photons,
each of energy m0*c2, or 511 KeV. Neither of the particles travel far,
so all the different interactions are indistinguishable from each other.
B.Energy Spectra
1.Photoelectric Absorption
The energy spectrum of a photoelectric absorption is very simple. The
spectrum is made up of the effects of the ejected photoelectron, and
the effects of the energy hole it creates. Photoelectron kinetic energy
is equal to the incident gamma ray energy minus its binding energy as
described in Equation 1. The effects of the binding energy show up as
7
8. an X-ray emitted as an outer shell electron deorbits or as an Auger
electron is ejected. Therefore, the energy spectrum for monoenergetic
gamma rays is an impulse function situated at the incident gamma ray
energy. See Figure 2 for a drawing of this.
Figure 2. Energy Spectra of Photoelectric Absorption for a
Monoenergetic Gamma Ray.
2.Compton Scattering
Normally all scattering angles will occur in the detector. This means
that the energies from the recoil electron will be distributed randomly
between 0 and Eγ. For one specific random gamma ray interaction,
the electron energy distribution will fit the curve shown in Figure 3.
Figure 3. Electron Energy Distribution of Compton Scattering from a
Monoenergetic Gamma Ray.
The point marked hν is the total energy of the original gamma ray (Eγ).
This energy is distributed between a recoil electron and a scattered
gamma ray photon. The energy Ec is the gap between the incident
gamma ray energy and the maximum Electron recoil Energy at Θ=180
degrees. Equation 6 describes this energy.
Eγ
E C = Eγ − E e − ( Θ = Π ) =
1 + 2 * Eγ
Equation 6:
511KeV
8
9. a)Compton Edge
If the incident gamma ray energy is much larger than ½ * 511 KeV,
then Equation 6 goes to a constant value of 256 KeV. Therefore the
Compton edge is about 256 KeV less than the incident gamma ray
energy (See Equation 7).
Equation 7: ECE = Eγ − 256keV
b)Backscatter
The backscatter peak is from source gamma rays that have interacted
by Compton scattering in the shielding material, and have been
deflected back into the detector. The energy of the Compton scatter is
described by Equation 2, and when the scattering angle is set to 180
degrees, Equation 2 simplifies to Equation 8. If the incident gamma
ray energy is much greater than ½ * the energy of an electron or
positron, then Equation 8 can be simplified into Equation 9.
Eγ
Eγ ' (Θ = 180) =
1 + 2 * Eγ
Equation 8:
511KeV
511KeV
Equation 9: Eγ ' (Θ = 180) = = 256 KeV
2
3.Pair Production
An ideal pair production energy spectrum is a delta function at the
incident gamma ray energy minus the total energy of an electron and a
positron. This difference is from the escape of the annihilation photons
when the positron combines with another electron and releases their
equivalent energy of 1.02 MeV.
Figure 4. Pair Production Energy Distribution from Monoenergetic
Gamma Ray Interaction
9
10. This energy peak is called a double escape peak, because both
annihilation photons escape. It is described by Equation 10.
Equation 10: E DE = Eγ − (2 * 511KeV )
C.Response functions
1.Small Detectors
A gamma ray detector is considered “small”, if its size is less than the
mean free path of the secondary gamma radiations produced in
interactions of the original gamma rays. This dimension is often
between 1 and 2 cm.
The energy range due to the different angles of scattering is called the
Compton continuum. The narrow peak corresponding to the
photoelectrons from the incident gamma ray is called the photopeak.
By definition, the small detector is sufficiently small that only single
interactions take place. If the gamma energy is high enough (much
greater than 1.02 MeV), pair production will occur. The electron and
positron kinetic energies will be deposited, and both resulting 1.02
MeV annihilation photons will escape.
2.Very Large Detectors
A gamma ray detector is considered “large” when all incident and
secondary gamma rays interact inside the detector volume. In the real
world, this is on the order of 10’s of centimeters. All the interactions
from the incident gamma ray occur so fast that they are electronically
indistinguishable. Therefore the spectrum that is detected looks like a
perfect photopeak, just as if the incident gamma ray had undergone
one photoelectric interaction.
3.Intermediate Size Detectors
Realistically detectors fall into the intermediate size range. These
detectors recover some of the secondary gamma ray energy that is
produced. Figure 5 shows a picture of such a detector.
10
11. Figure 5. Monoenergetic Gamma Ray Interactions in an Intermediate
Size Detector
The low to medium energy gamma rays consist of a Compton
continuum and a Full Energy Peak. The relative area under the Full
Energy Peak increases with decreasing gamma ray energy due to the
high Photoelectric Cross Section (σpe) at low energies.
At medium energies, multiple Compton scatters and the escape of the
final scattered photon can fill in the gap between the Compton edge
and the photopeak.
If the gamma ray energy is high enough to cause pair production, one
or both of the annihilation photons may escape without being detected.
This is called a single escape, and double escape peak respectively.
The energy of a single escape peak is described by Equation 11, while
the energy of a double escape peak is described by Equation 10.
11
12. Equation 11: E SE = Eγ − 511KeV
D.Energy Resolution
Equation 12 can be used to find the Energy Resolution of the detector,
where FWHM is the Full Width at Half Maximum count rate of the Full
Energy Peak, and Ho is the Mean Pulse Height of the same peak.
FWHM
Equation 12: R =
Ho
12
13. IV.Experimental Design and Procedure
A.2” x 2” NaI:Tl scintillator setup and procedure
The 2x2 NaI:Tl scintillator was connected to the MCA and support
electronics as shown in Figure 6.
HV
1000V
Osc.
2” x 2” NaI:Tl
p
Am
Pre-
32x
p
Am
Scintillator
MCA
Figure 6. 2” x 2” NaI:Tl scintillator Experimental Setup
First, the MCA was used to take a 5-minute background count in Live
Time Mode. This data was saved as filename MCA_Bkgnd in Aptec .S0
and .CSV format.
Second, a Cs-137 source was inserted in the detector and a 5-minute
count was taken. This data was saved as filename MCA_CS137 in
Aptec .S0 and .CSV format.
Third, a Co-60 source was inserted into the detector and a 5-minute count
was taken. This data was saved as filename MCA_Co60 in Aptec .S0 and
.CSV format.
Fourth, a Na-22 source was inserted into the detector and a 5-minute
count was taken. This data was saved as filename MCA_Na22 in
Aptec .S0 and .CSV format.
Fifth, an unknown source was inserted into the detector and a 5-minute
count was taken. This data was saved as filename MCA_Unknown#1 in
Aptec .S0 and .CSV format.
Sixth, a bonus source was inserted into the detector and a 5-minute count
was taken. This data was saved as filename MCA_Bonus in Aptec .S0
and .CSV format.
13
14. B.5” x 5” NaI:Tl scintillator setup and procedure
The 5” x 5” NaI:Tl scintillator was connected to an SCA, MCA, and the
associated electronics as shown in Figure 7.
HV
1000V
Osc.
5” x 5” NaI:Tl
p
Am
Pre-
4x
p
Am
SCA T/C
Scintillator
MCA
Figure 7. 5” x 5” NaI:Tl scintillator Experimental Setup
First, the SCA and the MCA were both used to take a 5-minute
background count. The MCA data was saved as filename SCA_Bkgnd in
Aptec .S0 and .CSV format.
Second, a Cs-137 source was inserted in the detector and the SCA was
used to take 1-minute counts of the source using an energy window of
0.05 Volts. The count was done until the spectrum flat lined after the Full
Energy Peak. The ending point was 1.5 volts. This data was saved as
filename SCA_Cesium-137.xls.
14
15. C.Equipment Used
Table 1 details a list of equipment used in this lab. Table 2 details the
manufacturer and activities of the sources used in the MCA portion of the
lab, and the mixed SCA/MCA portion of the lab.
Table 1: Equipment Type and Model Numbers used in Lab
Equipment Name Manufacturer, Model #
2”x2” NaI:Tl Scintillator Bicron, #155415
5”x5” NaI:Tl Scintillator 5MT4/5L
Preamplifier EG&G Ortec #113
High Voltage Supply (HV) Tennelec TC945
Amplifier (Amp) Canberra 2012
Single Channel Analyzer Canberra 2031
(SCA)
Counter/Timer (C/T) Canberra 1772
Multi-Channel Analyzer (MCA) Aptec Model 5008
SCA Oscilloscope Tektronix 2205-40
MCA Oscilloscope Tektronix 250
Table 2: Table of Radioactive sources used for lab
Source Activit Date of Manufacturer / Model#
y Manufacture
MCA
Sources
137
Cs 1 uCi 4/96 Oxford Model S-13
60
Co 1 uCi 4/96 Oxford Model S-13
22
Na 1 uCi 4/96 Oxford Model S-13
Unknown ? 4/96 ?
Extra Credit ? 4/96 ?
SCA Sources
137
Cs 1 uCi 12/17/1980 New England Nuclear
15
16. V.Results and Discussion
A.Single Channel Analyzer
1.Identify Peaks in Cs-137 Pulse Height Spectrum taken by SCA
From Table 4 in Appendix 4, it can be seen that the 662 KeV full
energy peak of Cs-137 is actually one of the gamma ray emissions
from its decay product Ba-137m. Looking at the plot of Cs-137
Source+Background Count Rate vs. Mean Window Voltage in
Appendix 3, this peak appears at around 1 Volt. It is known that this is
the Full Energy Peak, because it is the highest peak, and very well
defined. The next lowest peak appears at about 0.4 Volts, and is a
backscatter peak because it is poorly defined and is at 0.25 MeV or
less. The next lowest peak appears at around 0.15 Volts and is an X-
Ray peak from interaction of a primary gamma ray with the shielding
material. Finally the lowest peak is at about 0.1 volts, and is due to
instrumentation error.
2.Determine Detector Resolution
SCA Detector Resolution was determined from a plot of
Source+Background (S+B) Count rate vs. Mean Window Voltage for
Cs-137. The measured SCA count of B could not be subtracted from
S+B, because the B was from the entire energy spectrum of the
detector, while the S+B spectrum was binned in increments of 0.05
volts.
Instead, the B count rate under the full energy peak was visually
estimated as 9.9167 cps. Since the S+B Maximum Height was 210.05
cps, the Full Width, Half Maximum S+B level was found by dividing the
Maximum S+B by two. This yielded 105.025 cps.
Next a slope and y-intercept was found for each of the two lines that
defined either side of the S+B peak. The S+B (y value) of these two
equations were set to Ho/2, and a corresponding Mean Window
Voltage (x value) was calculated. Finally, the two Mean Window
Voltages were subtracted to find the FWHM. This value was used in
Equation 12 to calculate an energy resolution (R) of 0.05%. The
natural log of this Energy Resolution is –2.99. The FWHM found by
using the automated function on the Multi-Channel Analyzer was
7.89%, whose natural log R = 2.07. Per Knoll, page 331, the average
16
17. NaI(Tl) scintillator energy resolution for a sampling of several units of
the same design was between 10-11% (Knoll). The experimentally
measured Energy Resolution in Knoll, Table 10.17 is –2.1 for Cs-137
(Knoll).
3.Compare SCA Spectra with MCA Spectra
The SCA spectrum has far less resolution than the MCA spectrum.
The SCA spectrum completely missed one of the peaks at 27.96 KeV
or 4.93 KeV. It may have blended the two peaks into one peak
because our resolution was much lower with the SCA windowing
technique.
B.Multi-Channel Analyzer
1.Detector Resolution using Cs-137
From the MCA Paint Function, the detector resolution can be
calculated. For Cs-137, the Centroid (Ho) can be defined as 661.65
KeV (Hacker), while the FWHM is 52.48 KeV. Using Equation 12, this
gives an energy resolution of 7.93%. See Appendix 3 for plots and
denotation of peaks.
52.48 KeV
% Energy Re solution = *100%
661.65 KeV
2.Detector Resolution using Na-22
Using the MCA Paint function again, the detector resolution can be
calculated. For Na-22 Full Energy Peak, Ho is equal to 1274.5 Kev
(Hacker), and the FWHM is 37.34 KeV. Using Equation 12, this gives
an energy resolution of 2.93%. See Appendix 3 for plots and
denotation of peaks.
37.34 KeV
% Energy Re solution = * 100%
1274.5KeV
Table 3 is a summary of all the known and unknown feature energies
and channel numbers. The source plots with the features labeled can
be found in Appendix 3.
17
18. Table 3: Radionuclide Peak Definitions, Channel Numbers and
Energies
Radionuclid Peak Name Energy Channel Number
e (KeV)
Cs-137 Full Energy 661.65 688
Compton Edge 462.28 481
Backscatter 224.9 234
X-Ray 148.01 154
Instrumentation 19.22 20
Na-22 Full Energy 1274.5 1284.58
Annihilation 529.81 534
Compton Edge 1141.97 1151
Backscatter 200.42 202
Instrumentation# 19.84 20
1
Instrumentation# 9.92 10
2
Co-60 Full Energy #1 1332.5 1348
Full Energy #2 1173.9 1188
Compton Edge 946.98 940
Backscatter #1 217.49 167
Backscatter #2 321.3 277
Instrumentation# 69.32 10
1
Instrumentation# 78.76 20
2
Unknown Full Energy#1 385.2965 377.28
Full Energy#1 95.4458 93.46
Compton Edge
Backscatter 190.97 187
Compton Edge
Bonus Full Energy#1 2644.5831 2589.56
18
19. 3.Unknown Identification
The Energy Calibration Plot in Appendix 3 was made of the known
Photopeak Energies vs. MCA Channel number. The slope was
calculated from the Least Squares Regression of these known data
points. This slope, and a Y-Intercept of 0 were used to plot a best-fit
line along these original data points. The Y-Intercept was set to 0
because at Channel #0 we should get 0 energy. Next, the unknown
channels were put into the equation, and a corresponding energy was
output. The range for this energy was defined as FWHM/2. See
Appendix 3, Original Data for Plots.
From the fit, the unknown should have gamma ray energy of 385.3
KeV and gamma ray energy of 95.45 KeV with FWHM of 33.93 KeV,
and 22.7 KeV, respectively. Using the FWHM/2 search criteria,
elements with gamma ray energy of 385.3 +/- 17 KeV and 95.45 +/- 12
KeV were searched. The fractional emissions were arbitrarily chosen
to be greater than 0.01 for both of these gamma ray emissions.
The next sieve involved looking at the half-lives. Half-lives of less than
1 yr were eliminated. After eliminations, the result was Cf-249,
although upon closer inspection (See Appendix 4), the fraction of
emission (fp) for a 104.6 KeV photon is 0.02, while the fp for a 387.95
KeV photon is 0.66. Looking at the unknown curve in Appendix 3, the
lower energy peak has a higher count rate than the higher energy. If
this were Cf-249, the Higher Energy peak would show more counts.
4.Determine the Activity of the Cs-137
Equation 13 gives decrease in Activity after a time if the initial activity is
known.
Equation 13: A = Ao * e − λ*t
From Table 2, Cs-137 was 1 uCi (37KBq) on 4/96. At the date of the
lab, which was 2/28/01, the activity is calculated in Appendix 3 as
33052 Bq.
VI.Conclusions
A.2” x 2” scintillator compared to 5” x 5” scintillator
The instrumentation peak of the 5”x5” scintillator is almost non-existent
when compared to the 2”x2” scintillator. The resolution of the 5”x5” plot is
19
20. also finer. The photopeak shows many more counts were captured inside
of the 5”x5” detector that must have escaped the 2”x2” detector, or must
have undergone a Compton Scatter event instead of a Photoelectric
event. This is in agreement with the theory, which states that in a larger
detector, more of the interactions will look like Full Energy Peaks because
they lose all their energy inside the larger scintillator. A perfect detector
would have infinite size, and show only photoelectric peaks.
B.Method of determining Unknown
The plot of Photopeak Energy vs. Channel number yielded a strange
curvefit. The y-intercept was equal to approximately –41 KeV. At Channel
= 0, the Energy cannot be negative, so the Y-intercept was set to 0, which
raised the entire curvefit off from the data points. This could be a source
of error in the determination of the unknown source.
The identification of the unknown through passing nuclides of interest
through successive sieves is a good technique. It would be better to be
able to do a logic query on the nuclides of interest to make sure the count
rate of a high fractional emission photopeak was higher than a lower
fraction of emission photopeak.
The MCA Aptec program did not allow the subtraction of background.
Hence, the data file was manipulated in Excel and MCA for the necessary
results.
20
21. VII.References
Table of Authorities
Knoll, Glenn F, (1999), Radiation Detection and Measurement, Third
Edition.
Hacker, Charles, (March 1997). Radiation Decay Software, Version 2.
Fjeld, Robert, (8/24/2000), Clemson University EES610 Notes
http://www.cea.com/cai/augtheo/process.htm, “Auger Process”
21
